Question: Let the density f(x) be a decreasing function of |x|. Show that the shortest interval covering a given probability is symmetric about 0. Use this

Let the density f(x) be a decreasing function of |x|. Show that the shortest interval covering a given probability is symmetric about 0. Use this result to calculate the IF of the Shorth estimator (Problem 2.16a) for data with distribution f .

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